LIDAR DENSITY ANDSPACING SPECIFICATION
Version 1.0
Michael “Ty” Naus
Fugro Horizons, Inc.
Presented on behalf of the ASPRS PAD Lidar Committee

The Problem• “Nominal Pulse Spacing (NPS) of 1-2 meters…”1• “Nominal Pulse Spacing (NPS) – The estimated average
spacing of irregularly-spaced lidar points in both the alongtrack and cross-track directions…”2• How do we derive empirical NPS consistent withdesign NPS?
• How do we measure something as irregular aslidar points?
1 - U.S. Geological Survey National Geospatial Program Lidar Guidelines and BaseSpecification, Version 13
2 - FEMA Procedure Memorandum No. 61 – Standards for Lidar and Other High Quality
Digital Topography

The Goal• Simple• Easy to implement• Unbiased towards a sensor configurationand scan pattern• Consistent• Conform to existing standards,
specifications and guidelines• Flexible

The Procedure• Delaunay Triangulation– “Point” or “Pulse” spacing = average edge
length (2D) to all neighbor points• Voronoi Diagram– Point density = 1 / Voronoi polygon area

• Nominal– An LDSS measurement at a specified percentile
from a set of lidar points

TIN Elements• Nodes• Edges• Triangles• Convex Hull

Voronoi Diagram
The dual graphof theDelaunay
triangulation
for the same
set of points

Spacing Measurement
Spacing for the given
point =
1.314 +
2.050 +
2.027 +
1.237 +
0.888 +
1.011__________________= 8.527 / 6= 1.421Density Measurement

Nominal Values
We exclude
pointsassociated withthe convex hull
because they
have “long”
edges

1.

Sort spacing or density values from low to high2.

Extract a value at a percentile = nominal definition••

Point spacing (50%) = 1.447 = median

Point spacing (95%) = 1.566 (problematic small population)

Sample Area Selection• Use same checkpoints for vertical accuracy reporting
conforming to:– ASPRS Guidelines, Vertical Accuracy Reporting for Lidar Data,
Version 1.0– NDEP Guidelines for Digital Elevation Data, Version 1.0– U.S. Geological Survey National Geospatial Program Lidar
Guidelines and Base Specification, Version 13• These are convenient, thoroughly distributed, and fallwithin various land cover categories• Supplement with additional areas if neededPoint Population Selection•

The LDSS follows NPS criteria defined in USGS Lidar Guidelines andBase Specifications v13 where:– Single swath points– Located in center portion of swath (~90%)– First pulse returns? Can be used, but not best choice…
– Last pulse returns are much more likely to resemble the designNPS

First vs. Last Returns

Optech point cloud data, first returns, Fresno, California

First vs. Last Returns

Optech point cloud data, last returns, Fresno, California

First vs. Last Returns

Optech point cloud data, first returns, Fresno, CaliforniaFirst vs. Last Returns

Optech point cloud data, last returns, Fresno, California

Swath Checkpoints

Riegl point cloud data,Patterson, Georgia

Checkpoint Areas
Riegl point cloud data,
Patterson, Georgia

Keep things
simple and use abox for selectionof lidar points.
•Fast search•Small TIN’s•Consistent size
•Uniform land
cover categoryReporting
Checkpoint Area: 400.000
5105 points in search box used for statistics
Average Spacing: 0.296
Median Spacing: 0.296
Spacing Standard Deviation: 0.028
Spacing Variance: 0.00079
Spacing Skewness: -0.0058
Spacing Kurtosis: -0.5279
Nominal Spacing (95): 0.342

Reporting
Checkpoint Area: 400.000
336 points in search box used for statistics
Average Density (pts / unit squared ): 1.041
Median Density (pts / unit squared ): 1.052
Density Standard Deviation: 0.254
Density Variance: 0.06465
Density Skewness: 1.4432
Density Kurtosis: 1.4410
Nominal Density (95): 0.744

Leica point cloud data, last returns, forested land covercategory, Hagerstown, Maryland

Summary and Conclusions• The LDSS measurement method can be applied to any
regular or irregular point distribution• Defining a nominal value as a specified percentile
eliminates ambiguity and provides flexibility• Qualitative statistics provide additional insight into thecharacter of the distribution in a given area
• Supplement the ASPRS Vertical Accuracy and USGS v13
guidelines• Simple 3-step process

Questions?